C I n C B C D

CD = n.C d; (6)

and, consequently, the position of the needles which are found at A and
B are determined.

12. The question treated in Sec. 10, then, is simply solved. In fact, on
describing the circumference C b i a with any radius whatever, I shall
have

C B
n = -----; (7)
c b

and, consequently,

C I = n.C i (8)

13. As may be seen, the instrument composed of three firmly united
rulers is the simplest of all and easy to use. Any one can construct it
for himself with a piece of cardboard, and give the angle 2 [alpha] the
value that he thinks most suitable for each application. The greater
2 [alpha] is, the shorter is the distance at which we should put the
needles for a given point of meeting.

14 The jointed instrument may be constructed as shown in Figs 8, 9, and
10. The three pieces, A. B, and C, united by a pivot, O, in which there
is a small hole, are of brass or other metal. Rulers may be easily
procured of any length whatever. The instrument is Y-shaped. In the